# Difference between revisions of "2005 AMC 10B Problems/Problem 4"

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== Problem == | == Problem == | ||

+ | For real numbers <math>a</math> and <math>b</math>, define <math>a \diamond b = \sqrt{a^2 + b^2}</math>. What is the value of | ||

+ | |||

+ | <math>(5 \diamond 12) \diamond ((-12) \diamond (-5))</math>? | ||

+ | |||

+ | <math>\mathrm{(A)} 0 \qquad \mathrm{(B)} \frac{17}{2} \qquad \mathrm{(C)} 13 \qquad \mathrm{(D)} 13\sqrt{2} \qquad \mathrm{(E)} 26</math> | ||

== Solution == | == Solution == | ||

+ | <math>(5 \diamond 12) \diamond ((-12) \diamond (-5))\\ (\sqrt{5^2+12^2}) \diamond (\sqrt{(-12)^2+(-5)^2})\\ (\sqrt{169})\diamond(\sqrt{169})\\13\diamond13\\ \sqrt{13^2+13^2}\\ \sqrt{338}\\ \boxed{\mathrm{(D)\,13\sqrt{2}}}</math> | ||

== See Also == | == See Also == | ||

*[[2005 AMC 10B Problems]] | *[[2005 AMC 10B Problems]] |

## Revision as of 09:46, 29 June 2011

## Problem

For real numbers and , define . What is the value of

?

## Solution